We investigate the asymptotic behaviour of spinspin correlation functions for the integrable Heisenberg chain. To this end we use the Quantum Transfer Matrix (QTM) technique developed in ref. 1) which results in a set of non-linear integral equations (NLIE). In the case of the largest eigenvalue the solution to these equations yields the free energy and by modifications of the paths of integration the next-leading eigenvalues and hence the correlation lengths are obtained.